Stemless hemispherical resonator gyroscope

ABSTRACT

A vibrational gyroscope includes a piezoelectric ring having a central opening, and a hemispherical resonator having a central opening and mounted over the opening of the central opening of the piezoelectric ring. A plurality of electrodes delivers a voltage to the piezoelectric ring. A plurality of electrodes provides signal readout that corresponds to angular velocity. The hemispherical resonator can be glued to the piezoelectric ring. The hemispherical resonator preferably vibrates in the third vibration mode. A plurality of capacitive electrodes can be located at nodes and at antinodes of the vibration of the hemispherical resonator, and provide a signal readout that corresponds to the angular velocity. The piezoelectric ring is segmented, non-segmented, or includes an outer segmented portion and an inner non-segmented portion. The inner non-segmented portion can be used to excite the resonator into a vibration mode, and the outer segmented portion provides a readout signal and is used to adjust the vibration of the resonator. The piezoelectric ring includes a conductive coating used to conduct excitation voltage to the piezoelectric ring.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Provisional patentapplication Ser. No. 11/424,323, filed on Jun. 15, 2006, entitledSTEMLESS HEMISPHERICAL RESONATOR GYROSCOPE, which is incorporated byreference herein in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to vibrational gyroscopes, and moreparticularly, to high performance stemless hemispherical resonatorgyroscopes.

2. Background Art

Generally, the present invention is related to coriolis vibrationgyroscopes (CVGs) that typically use resonators made of quartz. Suchgyroscopes are described, for example, in U.S. Pat. Nos. 4,951,508,4,157,041, 3,719,074, 3,656,354, 6,357,296 and 5,383,362.

Numerous geometries of vibrational structures are known, and thesevarious geometries are commonly used in vibrational gyroscopes. Forexample, such structures include disks, rods, cylinders, hemispheres,etc. The vibrating elements can be made out of different materials, suchas ceramics, glass, quartz, metal, although the use of quartz or fusedsilica is most common. Usually, the best performance is provided bygyroscopes whose resonators have a high degree of axial symmetry, andthe resonator is made of a high-Q material. Since fused silica possessessuch characteristics as high degree of stability of elasticcharacteristics, and since a hemisphere has the highest degree of axialsymmetry of all the possible resonator geometries that are commonlyused, gyroscopes that use hemispherical quartz resonators tend to havethe highest precision. The Q factor of many such resonators can reachseveral million, while metal resonators rarely have a Q factor higherthan a few tens of thousands.

A CVG can also function as an angular velocity sensor that detectsrotation in two possible modes of operation—an open-loop mode, and aclosed-loop mode. The closed-loop mode is also sometimes referred to asa force-rebalance mode. The CVG can also function as an integratinggyroscope, also known as a “whole-angle mode,” which measures the angleof rotation of the gyroscope. See D. D. Lynch “Standard SpecificationFormat Guide and Test Procedure for Coriolis Vibratory Gyros,” September1998 meeting of the IEEE GAP in Stuttgart, Sep. 18-19, 1998.

In the simplest mode of operation, the open-loop mode, a standing waveis excited in the resonator in one of its modes of vibration (the drivemode). Usually, the second vibration mode is used, with an amplitudethat is maintained constant by an automatic gain control system (AGC).At the same time, a standing wave is produced within the resonator,which, in the second vibration mode of the resonator, has four nodes andfour anti-nodes. When the entire vibrating structure rotates about itsaxis, a coriolis force results, given by the equation F_(c)=2[Ω×V],where F_(c) is the coriolis force, Ω is the angular velocity of theresonator about its axis symmetry, and V is the linear velocity (in theradial direction, to and from the cylinder center axis). The coriolisforce F_(c) generates vibrations in the sense mode, which are measured,and whose amplitude is proportional to the angular velocity Ω. Thespatial orientation of the two modes is 45 degrees relative to eachother, for the second vibration mode.

When the CVG works in the open-loop mode, its bandwidth is directlyrelated to the Q factor of the coriolis vibration mode, in other words,to the damping time constant of the coriolis vibration mode. When the Qfactor is relatively high, for example, Q=10000, the bandwidth of theresonator is on the order of Δf=(πf_(c))/Q≈1.5 Hz if the frequency ofexcitation of the resonator f_(c)=5000 Hz. Such a gyroscope can, inpractice, only measure relatively constant angular velocities. Suchmeasurements are usually done, for example, using gyrotheodolite (agyro-optical instrument used to measure the azimuth fixed by atheodolite direction) when measuring the azimuth of a given direction.

To increase the bandwidth of the gyroscope, it is necessary to ensurethat the coriolis mode of vibration damps down relatively quickly, whichin turn leads to a lower Q factor of the measured vibration mode, and,consequently, to an increase in the gyroscope's bandwidth. The dampingdown of the measured vibration mode is done in the closed-loop mode, inother words, in the force rebalance mode. In this mode, the nodal pointsignal is measured, which is the same thing as the sense mode signal,and a negative feedback signal is generated, which compensates for thesignal arising in the nodes by supplying an anti-phase signal to one ofthe free nodes or to two diametrically opposite nodes out of the fournodes. Therefore, the measured mode of vibration is also suppressed,leading to a relatively low Q factor. With a Q factor of 100, thebandwidth would be approximately Δf=150 Hz. A CVG with such a bandwidthcan be used in many inertial systems that are mounted on moving objects.

In the whole-angle mode, the Coriolis force F_(c) that results from therotation of the resonator converts the energy of the vibration from thesense mode into the excitation mode and back, where the superposition ofthese two modes can be measured. Also, in this case, the standing wavein the resonator rotates together with the resonator. The angle ofrotation of the standing wave lags behind the angle of rotation of thegyroscope by a constant factor, which is defined only by the workingvibration mode. For the second mode of vibration, the constant factor isapproximately 0.32, for the third mode of vibration, the constant factoris approximately 0.25.

The design of the gyroscope that uses a hemispherical resonator, asdescribed above, suffers from a number of problems. One of theseproblems is the difficulty in mass-producing a relatively complex-shapedpart—the meniscus-shaped resonator with a stem, which is used formounting. Such a shape is relatively difficult to produce in massquantities. Another problem is that due to the complex shape,maintaining perfect axial symmetry of the resonator is extremelydifficult. Typically, during manufacture, the body of the resonator (thehemispherical portion) has thickness mismatches, which require extensiverebalancing and/or micro-machining to eliminate. This raises the cost ofthe resonator considerably, and increases the manufacturing time.

Another difficulty with such conventional gyroscopes is the need to usecapacitors for generating and detecting the vibration modes of theresonator. These capacitors typically require a relatively high voltage,on the order of several hundred volts, at times as much as 600 volts.Such high voltages are very inconvenient to work with, particularlywhere the overall device itself needs to be small. Also, the use of suchhigh voltages tends to result in a shorter life span of the device, anda faster wear on the electrical components of the device. Note that thedisadvantages described above apply to both the open-loop and theclosed-loop gyroscopes. Another problem is that due to the high voltagesinvolved, the power consumption of the device tends to be substantial.

Accordingly, there is a need in the art for a high precision vibrationgyroscope that addresses some or all of these problems.

BRIEF SUMMARY OF THE INVENTION

The present invention relates to an improved high precision stemlesshemispherical resonator gyroscope that substantially obviates one ormore of the disadvantages of the related art.

More particularly, in an exemplary embodiment of the present invention,a gyroscope includes a piezoelectric ring having a central opening, anda hemispherical resonator having a central opening and mounted over theopening of the central opening of the piezoelectric ring. A plurality ofelectrodes deliver a voltage to the piezoelectric ring. Anotherplurality of electrodes provide signal readout that corresponds toangular velocity. The hemispherical resonator can be glued to thepiezoelectric ring.

In an exemplary embodiment, the hemispherical resonator vibrates in thethird vibration mode. A plurality of capacitive electrodes are locatedat nodes and at antinodes of the vibration of the hemisphericalresonator, and provide a signal readout that corresponds to the angularvelocity. The piezoelectric ring can be segmented, non-segmented, or caninclude an outer segmented portion and an inner non-segmented portion.The inner non-segmented portion can be used to excite the resonator intoa vibration mode, and the outer segmented portion provides a readoutsignal and is used to adjust the vibration of the resonator. Thepiezoelectric ring can include a conductive coating used to conductexcitation voltage to the piezoelectric ring.

Additional features and advantages of the invention will be set forth inthe description that follows, and in part will be apparent from thedescription, or may be learned by practice of the invention. Theadvantages of the invention will be realized and attained by thestructure particularly pointed out in the written description and claimshereof as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and areintended to provide further explanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this specification, illustrate embodiments of the invention andtogether with the description serve to explain the principles of theinvention. In the drawings:

FIG. 1 illustrates the third vibration mode of a hemispherical resonatorand the locations of the electrodes at the vibrational nodes.

FIG. 2 is a schematic showing the excitation wave generation and thesignal readout of the angular velocity for a non-segmented piezoelectricring.

FIG. 3 illustrates the vibrational modes of the non-segmentedpiezoelectric ring when a periodic voltage is applied to it.

FIG. 4 illustrates the dependency of the amplitude of the vibration atthe equator of the resonator on the amplitude of the voltage applied tothe non-segmented ring.

FIG. 5 illustrates how the excitation waveform is driven for thesegmented piezoelectric ring, and the angular velocity signal readout.

FIG. 6 illustrates the nature of the vibration of the segmented ringwhen a periodic voltage is applied to it.

FIG. 7 illustrates the dependency of the vibration at the hemisphereequator on the amplitude of the voltage applied to the segmented ring.

FIG. 8 illustrates a diagram for controlling the excitation voltage andthe angular velocity signal readout for using a combinedsegmented-non-segmented piezoelectric ring.

FIG. 9 illustrates the dependency of amplitude and phase on frequencyfor a hemispherical quartz resonator glued to the piezoelectric ring.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to embodiments of the presentinvention, examples of which are illustrated in the accompanyingdrawings.

One embodiment of the present invention is a vibrational gyroscope witha hemispherical resonator that is stemless. The hemisphere is mounted ona piezoelectric ring, for example, using glue or epoxy. The ring itselfcan be manufactured from any material that has piezoelectric properties.The pole of the hemisphere is positioned directly over the opening ofthe piezoelectric ring. At the same time, the piezoelectric ring can beunitary, or can be segmented using a segmented coating (for example,silver), depending on which vibration mode is chosen, for example,second, third, etc. In the case of a segmented ring, each segment of thering receives a voltage to excite the resonator and/or (in the case ofclosed-loop operation) to control the standing wave, and, also possiblyto read out the signal that relates to the angular velocity. In the caseof a non-segment ring, a single voltage is supplied, providing an analogof the parametric excitation. To increase accuracy and sensitivity ofthe signal readout system, conventional capacitive sensors can belocated near the equator of the hemisphere.

Manufacturing of a stemless hemisphere greatly improves the smoothnessof the surface of the resonator, easily by a factor of 3-5. Furthermore,there is no need for a complex process of static and dynamic balancingof the resonator, which is necessary if the hemisphere deviatessubstantially from perfect axial symmetry. Furthermore, well-knownmanufacturing techniques used in lense manufacture can be used as well,simplifying the process and reducing manufacturing cost.

In order to initiate and sustain excitation of a quartz resonator byusing a piezoelectric ring, a voltage on the order of about 1 volt isneeded. Since the resistance of a piezoelectric ring is very high,typically on the order of tens of megaohms, the power consumptionrequired to keep the resonator in an excited state (i.e., vibrating) isa small fraction of a milliwatt, on the order of 1/100^(th) of amilliwatt.

When dissimilar elements, in this case, the piezoelectric ring and aquartz resonator, are joined, there is an interaction between thevibrating elements, caused by non-conservative forces generated when theresonator vibrates in the second vibration mode. This leads to an energydissipation of the excitation, in other words, to a reduction in the Qfactor of the resonator, and, consequently, to a loss of accuracy of thegyroscope. When the third excitation mode is used, this interaction isof a conservative nature, and does not lead to a significant energy lossor to a reduction in the Q factor. Therefore, there is no loss ofaccuracy of the gyroscope's measurements. Thus, the Q factor of aresonator described herein used in the second vibration mode is on theorder of 10⁵, while using the third vibration mode, the Q factor isapproximately 3×10⁶. Therefore, the third vibration mode has significantadvantages over the second vibration mode for the proposed device.Furthermore, in the third vibration mode, the imperfections in theresonator due to manufacturing tolerances and such (in other words, suchimperfections as ellipticity and thickness variation of the hemisphere)matter significantly less, and these have a smaller effect on the zerobias drift of the gyroscope.

Since the third vibration mode of the stemless hemisphere resonator hasconsiderably higher Q factor, the discussion below will be primarily interms of the third vibration mode, although one of ordinary skill in theart will readily appreciate how the discussion extends to othervibration modes as well. FIG. 1 illustrates the deformation of aresonator 102 when it vibrates in the third vibration mode. The standingwave has six antinodes that are oriented along the axes 1-1′ 3-3′ 5-5′,and six nodes oriented along the axes 2-2′, 4-4′ and 6-6′.

The process of vibrational excitation of the hemispherical resonator 102by using a piezoelectric ring (see 204 in FIG. 2) involves applying avoltage to the piezoelectric ring, such that a load that is evenlydistributed along the ring is generated, where the load is created alongthe inner boundary of the ring. The load is given by the equation:

$\begin{matrix}{f_{1} = {\frac{d_{31}E_{n}{hR}_{c}}{r_{0} + {w(\theta)}}U}} & (1)\end{matrix}$

Here, d₃₁—piezoelectric modulus of the piezoelectric ring, E_(n)—Young'smodulus of the piezoelectric ring, R_(c)—average radius of thepiezoelectric ring, h—average thickness of the piezoelectric ring,r=r₀+w(θ), r₀—inner radious of the piezoelectric ring, w(θ)—amplitude ofradial deformation, U—applied voltage.

A component of the force f₁ that is directed along the direction that isnormal to the surface of the hemisphere 102 (see FIG. 2) can berepresented as

${f_{n} = {f_{1}\frac{r}{R}}},$

where R is the radius of the hemispherical meniscus. As a firstapproximation, for a small displacement w, the force can be written as:

$\begin{matrix}{f_{w} = {{- \frac{d_{31}{Enn}_{c}U}{{Rr}_{0}}}{w(\theta)}}} & (2)\end{matrix}$

Given that

${{w(\theta)} = {{w_{0}\left( {\theta = \frac{\pi}{2}} \right)}\left( {n + {{Cos}\; \theta}} \right){tg}^{n}\frac{\theta}{2}}},$

where θ is the angular coordinate of the hemisphere, and at the point ofcontact between the hemisphere 102 and the ring 204 can be expressed as

${{w(\theta)} = {{w_{0}\left( {n + 1} \right)}\left( \frac{r_{0}}{2\; R} \right)^{n}}},$

where n—the order of the vibration mode (in this case, n=3), w₀(π/2) istherefore the amplitude of the deformation of the resonator 102 at itsequator.

If the voltage applied to the piezoelectric ring 204 is an AC voltage,with a frequency close to the third vibration mode U=U₀ Cos vt, then thedynamic equation—(Equation (3)) of the hemispherical resonator will havethe form:

{umlaut over (w)}″−{umlaut over (w)}+4Ω{dot over (w)}+κ ²(w ^(VI)+2w^(IV) +w″)+κ²ξ({dot over (w)} ^(VI)+2{dot over (w)} ^(IV) +{dot over(w)}″)=w″F ₀ sin vt  Equation (3)

where

${\kappa^{2} = \frac{E\; I}{\rho \; {SR}^{4}}},$

here E—Young's modulus of the resonator's material, I—rotational momentof inertia relative to the axis of symmetry, S—cross-sectional area,ρ—density of the material of the resonator, ξ—energy loss coefficient,and

$F_{0} = {\frac{d_{31}E_{n}R_{c}{hU}_{0}}{{Rr}_{0}\rho \; S}\left( {n + 1} \right)\left( \frac{r_{0}}{2\; R} \right)^{n}}$

is the applied force, and IV, VI refer to fourth and sixth derivative ofthe distance with regard to the circumferential coordinate.

Note that the force F₀ has a linear dependence on the applied voltageU₀. When the resonator 102 is not deformed, the distributed force (i.e.,force caused by residual charges in piezo material) is balanced by theinternal tension. When a force F₀ is applied to the resonator 102, theresonator 102 begins deforming. It should be noted that the resonatordeformation has a specific form—each vibration mode has its own patternof deformation. The third vibration mode has the highest Q factor, sinceit is energetically favorable. At the point where the resonator ismaximally deformed, the applied force has a greater value than at thepoint where the resonator is minimally deformed. In this process, therigidity of the attachment of the hemisphere 102 to the piezoelectricring 204 is important, since it is the rigidity of the glue couplingthat will determine the maximum permissible deformation amplitudew_(max)(θ). This is also due to the fact that the third vibration modeis the dominant mode in this case. Note that at the location where thehemisphere is mounted on the piezoelectric ring, the deformationamplitude of the second vibration mode is an order of magnitude greaterthan the deformation amplitude of the third vibration mode, and thisdetermines the nature of the interaction between the hemisphere and thepiezoelectric ring—whether it is conservative, or dissipative.

Considering the existence of the boundary conditions for the restrictedamplitude oscillation described by Equation 3, it is possible to findthe minimum value of the output voltage from the solution of Equation 3,which represents the angular velocity, and its dependence on theparameters of the sensing element, where exceeding that output voltageprovides for a stable excitation of the resonator, from the conditionF₀≧p, where p=18ξI/5ρSR⁴—decrement of the damping of the resonator,U_(0min)≈

, where K_(EM)=d₃₁E_(n)R_(c)h/r₀—coefficient of electro-mechanicaltransformation of the piezoelectric ring, a_(n)=(n+1)(r₀/2R).

Thus, the noise level of the excitation curve of the resonator, whichcan be seen in FIG. 4 (see dashed line) is defined by the losses in theresonator (ξ), the dimensional parameters of the resonator (the radiusR, rotational moment of inertia I), and on the parameter K_(EM) of thepiezoelectric ring.

If a non-segmented piezoelectric ring is used, it is possible to excitethe resonator and, in this case, control the standing wave, and thesignal readout can be done using traditional capacitive methods, asshown in FIG. 2, and as described, for example, in U.S. Pat. Nos.4,951,508, 4,157,041, 3,719,074 and 3,656,354. FIG. 2 illustrates ageneral view of the sensing element (in this case, a quartzhemispherical resonator, coupled to a piezoelectric ring), as well as aschematic of the control block 206 used for excitation, standing wavecontrol and angular velocity signal readout. The hemispherical resonator102 is mounted on the piezoelectric ring 204 close to the pole of thehemisphere, such that the small radius r₀ at the pole of the hemisphereis free, due to drilling a hole in the quartz hemisphere 102, with theradius r₀, which is equal to the radius of the opening 208 in thepiezoelectric ring 204. If a non-segmented ring is used, the excitationis accomplished by supplying a voltage U=U₀ sin 2πft to thepiezoelectric ring 204, which deforms due to the voltage, therebyapplying a force F₀ sin 2πft to the resonator 102. This, in turn, causesthe third mode of vibration, as discussed above. In this case, thecontrol signals are supplied to the capacitive electrodes, such as 4′,6′, 2′, while the signal readout is received from electrodes 2, 6, 4.See also FIG. 5, which shows the connections from the electrodes to thecontrol block 206, including the drivers/buffers 13, 14, 15, and 16, aswould be well-understood by one of ordinary skill in the art.

FIG. 3 illustrates the nature of the deformation when a non-segmentedring is used. The advantage of the proposed approach is, in part, inremoving a source of energy loss of the resonator where the resonatorhas manufacturing imperfections. Specifically, there is energydissipation through the pole of the hemispherical resonator, whosevibrational amplitude increases as the geometric mass imbalancesincrease. The energy is dissipated through the coupling of the resonatorto the piezoelectric ring. An additional advantage of the proposedapproach is in a substantial reduction in energy consumption, sinceconventional quartz resonators use an electrostatic field, whichrequires on the order of 600 volts to initiate the vibration, andapproximately 60 volts to sustain it. In the proposed approach, where astemless hemispherical resonator is used, the piezoelectric effect isused to initiate the vibration, and the maintenance of the vibrationrequires not more than one volt.

FIG. 4 illustrates the dependency of the vibration amplitude on thevoltage applied to the piezoelectric ring 204. As may be seen from FIG.4, one volt is sufficient to maintain a stable pattern of vibration inthe piezoelectric ring 204.

FIG. 5 illustrates a schematic used for excitation and control of thevibration, as well as for signal readout from a segmented piezoelectricring. As shown in FIG. 5, the signals are arranged in to groups ofthree, arranged at 120 degrees. The signals supplied to the sectors1-5-9 excite the third vibration mode. The signal picked up from sectors3-7-11 represent the response to excitation, and are used to maintainthe vibration by using positive feedback. The signals supplied tosectors 4-8-12 represent the correction signals, which suppress in phasecomponents in the nodes of the standing wave, which occur due toimperfections in the resonator manufacture. The same sectors 4-8-12receive a negative feedback signal, when the gyroscope works in a forcerebalance mode. The signals received from sectors 2-6-10 represent theuseful information, and correspond to the angular velocity. Thesesignals can be demodulated and averaged for a high signal-to-noiseratio.

FIG. 6 illustrates the nature of the deformation when a segmented ringis used. In this case, there is no need to use capacitive electrodes.This improves noise immunity to external electrostatic andelectromagnetic fields, and also reduces the requirements for shieldingfrom external electromagnetic fields, and for high tolerances during themanufacture of the housing of the gyroscope (the housing is not shown inthe figures). Typically, the housing can have a conductive filmdeposited on it. Note also that the distance between the housing and thesurface of the hemisphere should preferably be the same, as a functionof angular coordinate.

FIG. 7 illustrates the dependency of the amplitude of the vibration ofthe hemispherical resonator at its equator (measured using a capacitiveelectrode) on the voltage applied to the corresponding segment of thepiezoelectric ring, which is located underneath that electrode. Themonotonic (generally parabolic) dependency illustrated in FIG. 7illustrates how the amplitude of the vibration can be controlled usingthe applied voltage.

FIG. 8 illustrates a schematic for excitation and controlling a combinedsegmented/non-segmented piezoelectric ring. One portion of thepiezoelectric ring, the inner portion, is not segmented, while the outerportion of the piezoelectric ring is segmented. In this case, thenon-segmented inner portion of the ring is used only to excite theresonator as shown in FIG. 3, and excites the resonator using the forcesillustrated in FIG. 2. To control the standing wave and to correct thestanding wave, the segments are used, as also illustrated in FIG. 5.Signal readout from the piezoelectric ring can be done using thecorresponding segment of the ring, as well as using the additionalcapacitive electrodes shown in FIG. 2. When a non-segmented ring is usedfor excitation, the third vibration mode is excited because the voltagethat is supplied has a frequency that is close to the natural frequencyof the third vibration mode, as well as because this mode has a high Qfactor (for example, compared to the second vibration mode), and istherefore energetically favorable. At the same time, segments 1, 5 and9, used in the embodiment of the segmented ring, are now free, and canbe used, for example, to correct the asymmetry of the amplitude of thestanding wave, which is due to imperfections in the manufacturing of thering. In the case of the embodiment illustrated in FIG. 8, it ispossible to ensure a high sensitivity to angular velocity, which is acharacteristic of capacitive sensors, and a high signal-to-noise ratio,due to the processing of two separate signals—a piezoelectric signal,and a capacitive signal. Furthermore, this provides an additionalindependent measurement channel that can be used to measure the angularvelocity, and can also be used to determine failures and gliches in thesensor, for example, by comparing the two signals. This leads to ageneral increase in the reliability of the gyroscope.

FIG. 9 illustrates the dependency of the amplitude and phase on thefrequency of excitation, for the quartz hemispherical resonator that ismounted on a piezoelectric ring using glue attachment. Measurements werenormalized by dividing all measured values U_(b) by the maximum valueU_(max), obtained at resonant frequency and represented as a graphU_(b)/U_(max) versus the excitation frequency. In this example, thepiezoelectric ring has a diameter of 20 milimeters, while the diameterof the quartz hemisphere is 30 milimeters. The opening in the ring hasthe same diameter as the opening in the hemisphere resonator, and bothare 4 milimeters. In this example, the Q factor of this resonator is1.2×10⁶, while the frequency of the third vibration mode is 13760.7 Hz.

Having thus described embodiments of the invention, it should beapparent to those skilled in the art that certain advantages of thedescribed method and apparatus have been achieved. It should also beappreciated that various modifications, adaptations, and alternativeembodiments thereof may be made within the scope and spirit of thepresent invention. The invention is further defined by the followingclaims.

1. A gyroscope comprising: a non-segmented piezoelectric ring having acentral opening; a hemispherical resonator having a central opening andmounted over the central opening of the piezoelectric ring so that bothcentral openings are aligned; a plurality of electrodes delivering avoltage to the piezoelectric ring; and a plurality of electrodes mountedon the piezoelectric ring and providing a signal readout thatcorresponds to angular velocity.
 2. The gyroscope of claim 1, whereinthe two central openings have substantially the same radii.
 3. Thegyroscope of claim 1, wherein the plurality of electrodes on thepiezo-electric ring are mounted on a side of the piezoelectric ringfacing the hemispherical resonator.
 4. The gyroscope of claim 1, whereinthe hemispherical resonator is glued to the piezoelectric ring.
 5. Thegyroscope of claim 1, wherein the hemispherical resonator vibrates in athird vibration mode.
 6. The gyroscope of claim 1, further comprising aplurality of capacitive electrodes at nodes and at antinodes of thevibration of the hemispherical resonator.
 7. The gyroscope of claim 4,wherein the capacitive electrodes provide a signal readout thatcorresponds to the angular velocity.
 8. The gyroscope of claim 1,wherein the piezoelectric ring includes a conductive coating used toconduct excitation voltage to the piezoelectric ring.
 9. A gyroscopecomprising: a sensing element comprising a hemispherical resonatorcoupled to a piezoelectric ring; a plurality of electrodes delivering avoltage to the piezoelectric ring; and a plurality of electrodes on thepiezoelectric ring underneath the hemispherical resonator and on a sideof the piezoelectric ring facing the hemispherical resonator, andproviding a signal readout that corresponds to angular velocity, whereinthe hemispherical resonator has a central opening at its pole that ispositioned over the central opening of the piezoelectric ring andsubstantially aligned with the central opening of the piezoelectricring, and wherein the piezoelectric ring includes an outer segmentedportion and an inner non-segmented portion.
 10. The gyroscope of claim9, wherein the inner non-segmented portion is used to excite theresonator into a vibration mode, and the outer segmented portionprovides a readout signal and is used to adjust the vibration of theresonator.
 11. The gyroscope of claim 9, wherein the hemisphericalresonator is glued to the piezoelectric ring.
 12. The gyroscope of claim9, wherein the hemispherical resonator vibrates in a third vibrationmode.
 13. The gyroscope of claim 9, wherein a coupling between thehemispherical resonator and the piezoelectric ring is substantiallylossless
 14. The gyroscope of claim 9, further comprising a plurality ofcapacitive electrodes at nodes and at antinodes of the vibration of thehemispherical resonator.
 15. The gyroscope of claim 9, wherein the innernon-segmented portion is used to excite the resonator into a vibrationmode, and the outer segmented portion provides a readout signal and isused to adjust the vibration of the resonator.
 16. A gyroscopecomprising: a non-segmented piezoelectric ring having a central opening;a hemispherical resonator having a central opening and mounted over thecentral opening of the piezoelectric ring so that both central openingsare aligned, and wherein a coupling between the hemispherical resonatorand the piezoelectric ring is substantially lossless; a plurality ofelectrodes delivering a voltage to the piezoelectric ring and mounted ona side of the piezoelectric ring facing the hemispherical resonator; anda plurality of capacitive electrodes mounted at nodes and at antinodesof vibration of the hemispherical resonator, and providing a signalreadout that corresponds to angular velocity.